NEWARK, N.J. — It was a globe-trotting romance: a handsome American working as a model in Italy falls in love with a Brazilian beauty studying fashion design in Milan. They marry in 1999, settle in the tony New Jersey shore town of Red Bank, and have a son.

Four years later, the couple”s relationship begins to change from an international love affair into a diplomatic nightmare.

The woman, Bruna Bianchi, took the couple”s son to visit her relatives in Brazil in 2004 but never returned. The boy”s father, David Goldman of Tinton Falls, N.J., has been battling to get back his son ever since.

While the Goldman case has been prominent in recent news coverage, it isn”t the only dramatic custody case being fought across international borders. The U.S. State Department says such parental abductions involving American children are rising. There were more than 1,000 new cases of American children taken by a parent to another country last year — a 35 percent increase over 2007, according to the department.

The international tug-of-wars get even more difficult to resolve when nations disagree on which parent should keep a child.

“It”s not just a U.S. trend, it”s a worldwide trend,” said Julie Furuta-Toy, director of the Office of Children”s Issues at the U.S. Department of State.

“In the long term, it is the children who suffer,” she said.

The State Department has been looking into what may account for “a sharp increase” in abduction cases involving American children, Furuta-Toy said.

The unstable U.S. economy may be one factor, she said. It has led to layoffs of foreign-born workers, which might prompt a parent to return to his or her home country and take a child with them. Other possible reasons are the increase in binational marriages and more awareness of parental child abductions, Furuta-Toy said.

Charles Abut, a family law specialist in New Jersey, said he has seen the number of international custody disputes rise in tandem with globalization and intercultural marriage during the past decade.

“We”re living in a much more global world, the distances aren”t as great, and we have many instances of people traveling to different countries,” Abut said. “When you couple international travel with a divorce, it”s absolutely the case that these — and let”s call them abductions — happen more often.”

Cases where a parent takes an abducted child to a foreign country can be difficult and costly to litigate, involve numerous legal systems and sometimes drag on for years, leaving children in limbo.

Even cases governed by the Hague Convention on International Abductions, a treaty that addresses how to handle children taken across international borders without a parent”s consent, are not always resolved quickly. That includes the Goldman case, which has dragged on for five years, even though Brazil and the U.S. are signatories to the treaty.

In the Goldman case, David Goldman”s wife divorced him shortly after taking their son to Brazil, where she remarried and died last year after giving birth to a daughter. Sean Goldman, 9, has been living with his Brazilian stepfather and other relatives for five years, despite numerous court orders that the boy be returned to his American father.

The case has reached the highest levels of the Brazilian and U.S. governments, with President Barack Obama asking that the boy be returned to Goldman, and Brazil”s Supreme Court recently rejecting a challenge to a lower court order that the boy be returned to his biological father. But the boy”s return to the U.S. is likely to be delayed by an appeal by his Brazilian relatives.

State Department officials say the goal always is to resolve such cases quickly, so children don”t suffer a prolonged separation from a parent.

In extreme cases, a child may be left without either parent.

Maria Jose Carrascosa has been in a New Jersey jail for more than two years for defying a court order to return her daughter to the United States from Spain, where Carrascosa took her to live with her maternal grandparents during a divorce.

A U.S. court granted her ex-husband, Peter Innes of Hasbrouck Heights, N.J., sole custody of the child, while Carrascosa has an order from a Spanish court that the girl remain in Spain until she”s 18. The girl still lives with her grandparents in Spain, and has not seen either parent in years.

U.S. State Department officials, judges from the New Jersey county where Carrascosa is incarcerated, and Spanish authorities traveled recently to The Hague to mediate a solution. The results of the meeting have not been made public.

International parental abduction cases can be found across the United States, said U.S. Rep. Christopher Smith, a Republican from New Jersey who has been advocating for Goldman.

Smith said after he proposed legislation that would attach punitive damages — such as revoking trade preferences — to nations that harbor parental abductors, people across the country starting contacting him about their desperate plights.

“What I”ve told David (Goldman) is by his heroic efforts to get his son back, he”s not only brought hope and renewed activity for other families, he”s lifted the veil off this egregious problem for the United States Congress,” Smith said. “This is a serious issue globally that Congress, the White House and the State Department has to do much more than we”ve done to date.”